In a written statement to Parliament, Mr Reid said the policy had been a success because migrant workers had filled skills gaps.

But he acknowledged some schools had had to cope with a "significant rise" in pupils, while some councils had reported overcrowding in private housing.

The new policy will be reviewed annually. Mr Reid said policing it would be challenging, but those caught working illegally would face on-the-spot fines, with hefty penalties for their employers.

But shadow home secretary David Davis said allowing any EU citizen to work in the UK if they are self-employed was a "big loophole" and said there was no way of stopping "undesirables" living in the UK.